This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. Primary support for the subproject and the subproject's principal investigator may have been provided by other sources, including other NIH sources. The Total Cost listed for the subproject likely represents the estimated amount of Center infrastructure utilized by the subproject, not direct funding provided by the NCRR grant to the subproject or subproject staff. The overall goals of this proposed research are to a) improve the design and application of computational methods necessary to process data obtained by optical probes and b) extend our capacity to analyze and image heterogeneous tissue structures on sub-millimeter to centimeter length scales. The vast majority of methodologies currently used to model the transport of light in tissue (the forward problem) and to determine the optical properties of heterogeneous tissue structures (the inverse problem) rely heavily on standard or enhanced optical diffusion models, supplemented by the occasional use of detailed Monte Carlo simulations. We are developing advanced Monte Carlo methods that lead to faster, more accurate and, in some instances, detailed global solutions of tissue/light transport problems. Novel methods for modeling approximate solutions of both forward and inverse problems have also been developed. Effort has concentrated on the selective application of these methods to forward and inverse problems of direct relevance to LAMMP core program technologies and to related collaborative research. Reported elsewhere is recent progress on "Perturbation Monte Carlo Techniques for Diffuse Photon Transport", "Monte Carlo Modeling for Diffuse Photon Migration", and "Condensed History Monte Carlo Algorithms". Here we report on a recent breakthrough in the development of adaptive Monte Carlo algorithms (i.e., algorithms capable of learning that achieve geometric convergence for general transport problems. We have discovered a new geometrically convergent method for estimating the averages of the detailed space-angle distribution of light over arbitrary decompositions of the tissue phase space. This new technique has great potential for bringing accurate radiative transport computational methods into more routine use for biomedical and other applications in biology and medicine.